Write an equation describing the relationship of the given variables. $y$ varies directly as the fourth power of $x$ and when $x=3, y=324$

Step 1 ：Write an equation describing the relationship of the given variables: $y=kx^4$

Step 2 ：Given: when $x=3$, $y=324$

Step 3 ：Substitute the given values into the equation: $324=k(3)^4$

Step 4 ：Solve for $k$: $k=\frac{324}{3^4}=4.0$

Step 5 ：Substitute the value of $k$ back into the equation: $y=4x^4$

Step 6 ：\(\boxed{y=4x^4}\)